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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=-5/2, a2>=-5/2 > For fixed z and a1=-5/2, a2=-3/2, a3>=-3/2 > For fixed z and a1=-5/2, a2=-3/2, a3=7/2 > For fixed z and a1=-5/2, a2=-3/2, a3=7/2, b1=1





http://functions.wolfram.com/07.27.03.a9d5.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), -(3/2), 7/2}, {1, 4}, z] == (128 (64 + 206 z + 2367 z^2 + 463670 z^3 + 647848 z^4 + 16128 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/(1091475 Pi^2 z^3) + (1/(1091475 Pi^2 z^3)) (128 Sqrt[1 - z] (-64 - 222 z - 2430 z^2 - 226685 z^3 - 217728 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(1091475 Pi^2 z^3)) (128 (-64 - 206 z - 2367 z^2 - 463670 z^3 - 647848 z^4 - 16128 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (64 Sqrt[1 - z] (64 + 222 z + 2430 z^2 + 226685 z^3 + 217728 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(1091475 Pi^2 z^3) + (64 (64 + 190 z + 2313 z^2 + 293663 z^3 + 378860 z^4 + 8064 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(1091475 Pi^2 z^3)










Standard Form





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MathML Form







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type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 463670 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2367 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 206 </cn> <ci> z </ci> </apply> <cn type='integer'> 64 </cn> </apply> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1091475 </cn> <apply> 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<times /> <cn type='integer'> 222 </cn> <ci> z </ci> </apply> <cn type='integer'> 64 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1091475 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 8064 </cn> <apply> <power /> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02